The NLF can also be computed microscopically, using EDF. The covariant EDFs are known to describe spatially localized alpha structures in light nuclei [1]}, [2]}, visible in their nucleonic density. This is less the case with Skyrme EDF, where no such structure spontaneously appears in the ground-state density. The difference is due to the depth of the confining mean-field potential, which is larger in the covariant case, being based on the scalar and vector fields, related to the saturation properties of nuclei [1]}. It should be noted that the covariant EDF calculations realized at the projected-GCM level, also allowed to successfully describe the rotational bands observed in \(^{20}\) Ne, as well as
in \(^{12}\) C for the Hoyle state [4]}, [5]}. In the case of Skyrme EDF, spatially localized structure in the densities can be obtained only at very large deformation of very high spin states [6]}, [7]}.
